[Haskell-cafe] instance Monoid a => Monad ((,) a)

[David Feuer]

Bool is also a monoid under xor.

On Mon, Aug 5, 2019, 4:34 PM Jinxuan Zhu <zhujinxuan at gmail.com> wrote:

> Hi, I think the error message says there is no Monoid for Bool.  It is
> because Bool can be monoid by either || or && operations, which would lead
> to ambiguity if Bool is monoid by default.
>
> You can:
> 1. use Maybe Unit instead
> 2. (overkill) Define AndMonoid Bool newtype and use DeriveVia and coerce
>
>
>
> On Fri, Aug 2, 2019 at 7:39 PM Benjamin Franksen <ben.franksen at online.de>
> wrote:
>
>> I wanted to define a simple Monad instance for (Bool,) as
>>
>> instance Monad ((,) Bool) where
>>   return x = (False, x)
>>   (True, x) >>= k = (True, snd (k x))
>>   (False, x) >>= k = k x
>>   -- or: (b, x) >>= k = let (c, y) = k x in (b||c, y)
>>
>> The idea was to keep track of whether functions change their input value
>> or not.
>>
>> To my astonishment I found that this definition overlaps with an
>> existing one. GHC tells me
>>
>> x.hs:2:10: error:
>>     • No instance for (Monoid Bool)
>>         arising from the superclasses of an instance declaration
>>     • In the instance declaration for ‘Monad ((,) Bool)’
>>   |
>> 2 | instance Monad ((,) Bool) where
>>   |          ^^^^^^^^^^^^^^^^
>>
>> x.hs:2:10: error:
>>     • Overlapping instances for Monad ((,) Bool)
>>         arising from a use of ‘GHC.Base.$dm>>’
>>       Matching instances:
>>         instance Monoid a => Monad ((,) a) -- Defined in ‘GHC.Base’
>>         instance Monad ((,) Bool) -- Defined at x.hs:2:10
>>     • In the expression: GHC.Base.$dm>> @((,) Bool)
>>       In an equation for ‘>>’: (>>) = GHC.Base.$dm>> @((,) Bool)
>>       In the instance declaration for ‘Monad ((,) Bool)’
>>   |
>> 2 | instance Monad ((,) Bool) where
>>   |          ^^^^^^^^^^^^^^^^
>>
>> [one more similar overlap error elided]
>>
>> But I could not find the
>>
>>   instance Monoid a => Monad ((,) a)
>>
>> documented anywhere in the base package. Should I look harder? Or is
>> this instance accidentally leaking from GHC.Base?
>>
>> Eventually, through some experimenting I found that if I replace Bool
>> with Any, then the existing instance seems to do what I want.
>>
>> Cheers
>> Ben
>>
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